2021/07/19 by Michal Zwierzynski, Zwierzyński, M.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2107.08605
openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the notion of the singular evolutoid set which is the set of all singular points of all evolutoids of a fixed smooth planar curve with at most cusp singularities. By the Gauss-Bonnet Theorem for Coherent Tangent Bundles over Surfaces with Boundary (Theorem 2.20 in [4]) applied to the extended front of evolutoids of a hedgehog we obtain an integral equality for smooth periodic curves.